I’m not overly great on curtains but in past few years I’ve taken to removing curtain tape, cutting it down and sewing it back on. Attempt to move hems up have always been disastrous on lined curtains for me. I always take note of how it’s constructed as i deconstruct. I generally sew back on the existing tape.
before I do it I sew on my machine in the widest stitch across the entire width of the fabric a tacking line, holds the curtain together with its lining whilst I cut off top etc, I remove it when I’ve shortened it.
however, in our local town there’s a chap who alters all sorts of things very reasonably and I’m thinking I’ll probably see how much he charges next time I want to do it, mind you ours are all simple curtains.
Ive cut curtains in half vertically to fit and it’s worked well. I generally hang them up and play around with how they look. Somewhere like John Lewis can probably advise on heading tape and widths of fabric depending on the gathering required. Thickness of the curtain fabrics and linings impacts on the look of the gathered tapes.
I made a mistake recently and wanted tightly gathered pencil tape pleats but the gathering was loose as the fabric and lining was thinner (and six inches narrower per curtain) than my old curtains so doesn’t look as good.
I’ve made simple envelope cushions (no zip) from left over fabrics and in our dining room I made a table runner too.
if your drop is to the floor I think I’d probably take up from bottom with a wide hem and possibly add some curtain weights into the corners as a slightly wonky bottom hem at carpet level probably wouldn’t show. (But this depends on how the hem is finished on lined curtains and is generally why I shorten from the top).
I often find good tutorials on YouTube.
there’s probably a right way to do it but I’m one that tends to just give it a go, but always measure twice and only cut once! Or in my case probably measure 20 times and cut once.